Stability of compact breathers in translationally-invariant nonlinear chains with flat dispersion bands

  title={Stability of compact breathers in translationally-invariant nonlinear chains with flat dispersion bands},
  author={Nathan Perchikov and Oleg V. Gendelman},
  journal={Chaos Solitons \& Fractals},
1 Citations



Flat bands and compactons in mechanical lattices.

This work considers a discrete mechanical system with flat dispersion bands, in which the nonlinearity exists due to impact constraints, and considers a smooth nonlinear lattice with linearly connected massless boxes, each containing two symmetric anharmonic oscillators.

Compactification tuning for nonlinear localized modes in sawtooth lattices.

The properties of nonlinear localized modes in sawtooth lattices are discussed in the framework of a discrete nonlinear Schrödinger model with general on-site nonlinearity, and their stability over large parameter regimes is shown.

Single and double linear and nonlinear flatband chains: Spectra and modes.

We report results of systematic analysis of various modes in the flatband lattice, based on the diamond-chain model with the on-site cubic nonlinearity, and its double version with the linear on-site

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In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the

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Self-accelerating waves in conservative systems, which usually feature slowly decaying tails, such as Airy waves, have drawn great interest in studies of quantum and classical wave dynamics. They

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  • G. James
  • Mathematics, Physics
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2018
An extensive numerical exploration of travelling breather profiles for p = 5/2 suggests that these solutions are generally superposed on small amplitude non-vanishing oscillatory tails, except for particular parameter values where they become close to strictly localized solitary waves.

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Linear wave equations on flat band networks host compact localized eigenstates (CLS). Nonlinear wave equations on translationally invariant flat band networks can host compact discrete breathers -

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